A three-dimensional distinct lattice spring method is a numerical model in which matter is discretized into individual particles connected by springs. The connected springs include a normal spring and a shear spring for each pair of particles and their stiffnesses of the springs are calculated for a pair of fixed values of the Young's modulus and the Poisson's ratio. The very simple cubic structure of particles is introduced and three different types of spring setup to connect particles are assumed to model a linear elastic medium. The relationship between stiffness of these micro springs and the macro elastic constants must be examined to simulate not only static deformation and failure of rock materials but also dynamic fracturing problems. In this paper, a relation based on the classical elastic theory is introduced and simple two numerical examples will be presented, the first is the uniaxial compression loading of parallel-shaped cell model and the second is a cantilever model subjected to bending. The aim of the second simulation is to study more complex stress state which will be produced in the medium, tensile, compression and shear. These numerical examples are presented to show and discuss the abilities of the method in modeling elastic problems.

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